Gene expression is often regulated by the binding of small RNAs or proteins to messenger RNA;examples include mRNA splicing, microRNA, and degradation signals. Making more accurate predictions will help uncover the function and cellular activity of binding and splicing mRNA. We propose to: (1) Develop physical-chemical models of small RNAs and proteins binding that modulate gene expression through mRNA binding. Our recently developed oligo-binding algorithm BINDIGO efficiently computes binding free energies. We aim to improve the accuracy with which binding sites can be identified. (2) Improve models of mRNA splicing to understand the role of thermodynamics in alternative splicing and intron/exon segregation, and correlations in the codon frames where introns begin. Our preliminary results show unexpected and significant correlations;they also show energetic biases which may explain how cells find splice junctions. (3) Discover how pre-existing secondary structure influences binding events, and how binding modifies remaining secondary structures. (4) Expand RNA folding algorithms to include binding events. It is estimated that at least 15% of genetic point mutations result in incorrectly spliced mature mRNA. By elucidating the mechanisms and improving the predictions of splicing, it may be possible to design therapeutics. And, since identifying splice sites is a bottleneck in finding genes, improvements in this area can contribute to revealing genomic information. The proposed algorithms have the potential for wider application: predicting anti-sense gene therapies, RNA interference, retro-transposon recognition, RNA regulation of gene expression, and systematic errors in gene chip microarrays. We propose to model and compute how binding small RNAs and proteins modulates gene expression, in particular mRNA splicing.